1.
In the 1996 regular baseball season, the World Series Champion New York Yankees played 80 games at home and 82 games away. They won 49 of their home games and 43 of the games played away. We can consider these games as samples from potentially large populations of games played at home and away. How much advantage does the Yankee home field provide?
a. Find the proportion of wins for the home games. Do the same for the away games.
b. Find the standard error needed to compute a confidence interval for the difference in the proportions.
c. Compute a 90% confidence interval for the difference between the probability that the Yankees win at home and the probability that they win when on the road. Are you convinced that the 1996 Yankees were more likely to win at home?
2.
The state agriculture department asked random samples of Indiana farmers in each county whether they favored a mandatory corn check off program to pay for corn product marketing and research. In Tippecanoe County, 263 farmers were in favor of the program and 252 were not. In neighboring Benton County, 260 were in favor and 377 were not.
a. Find the proportions of farmers in favor of the program in each of the two counties.
b. Compute a 95% confidence interval for the difference between the proportions of farmers favoring the program in Tippecanoe County and in Benton County. Do you think opinions differed in the two counties?
3.
A study of chromosome abnormalities and criminality examined data on 4124 Danish males born in Copenhagen. The study used the penal registers maintained in the offices of the local police chiefs and classified each man as having a criminal record or not. Each was also classified as having the normal male XY chromosome pair or one of the abnormalities XYY or XXY. Of the 4096 men with normal chromosomes, 381 had criminal records, while 8 of the 28 men with chromosome abnormalities had criminal records. Some experts believe that chromosome abnormalities are associated with increased criminality. Do these data lend support to this belief? Report your analysis and draw a conclusion.
A recent study examined the association between high blood pressure and increased risk of death from cardiovascular disease. There were 2676 men with low blood pressure and 3338 men with high blood pressure. In the low-blood-pressure group, 21 men died from cardiovascular disease; in the high-blood-pressure group, 55 died.
a. Compute the 95% confidence interval for the difference in proportions.
b. Do the study data confirm that death rates are higher among men with high blood pressure? State hypotheses, carry out a significance test, and give your conclusions.
4.
Find the p-value for each by filling in the table (don’t forget to complete the calculator command):
|
Degrees of Freedom |
x2 |
Calculator Command |
p-value |
|
4 |
5 |
x2cdf( |
|
|
4 |
10 |
x2cdf( |
|
|
4 |
15 |
x2cdf( |
|
|
4 |
20 |
x2cdf( |
|
|
3 |
15 |
x2cdf( |
|
|
4 |
15 |
x2cdf( |
|
|
5 |
15 |
x2cdf( |
|
|
6 |
15 |
x2cdf( |
|
5.
Sarah is running a chi-squared Goodness of Fit test to test whether the claimed proportions of candy colors in assorted bags of candy are different than claimed by the company. She takes a random sample of 300 pieces of candy from assorted bags. The company claims the following proportions of colors in assorted bags:
|
Green |
Yellow |
Red |
Blue |
|
0.2 |
0.3 |
0.3 |
0.2 |
What are the expected results of each color?
6.
A regular 6-sided die is tossed 200 times with the faces turning up as follows:
|
Number |
1 |
2 |
3 |
4 |
5 |
6 |
|
Frequency |
34 |
28 |
35 |
31 |
31 |
41 |
Is there reason to suspect that the die is not fair? Run a complete test.
7.
What does the chi-squared test of independence really test?
8.
When working with a two-way table, describe how you find the expected counts for each cell in the table.
9.
A survey was conducted of 200 people and their responses were categorized by party affiliation and opinion on gun control. The results are shown in this table:
|
Observed |
Favor |
Oppose |
Unsure |
Total |
|
Democrat |
44 |
48 |
18 |
110 |
|
Republican |
32 |
48 |
10 |
90 |
|
Total |
76 |
96 |
28 |
200 |
a. Fill in the table below with the expected counts.
|
Expected |
Favor |
Oppose |
Unsure |
Total |
|
Democrat |
|
|
|
110 |
|
Republican |
|
|
|
90 |
|
Total |
76 |
96 |
28 |
200 |
b. Based on this sample, does a person’s opinion on gun control depend on party affiliation, at the .05 level of significance?
10.
There are four major blood types in humans: O, A, B, and AB. In a study conducted using blood specimens from the Blood Bank of Hawaii, individuals were classified according to blood type and ethnic group. The ethnic groups were Hawaiian, Hawaiian-white, Hawaiian-Chinese, and white. Assume that the blood bank specimens are random samples from the Hawaiian populations of these ethnic groups.
|
Ethnic Group —
Blood Type |
Hawaiian |
Hawaiian White |
Hawaiian Chinese |
White |
|
O |
1,903 |
4,469 |
2,206 |
53,759 /div> |
|
A |
2,490 |
4,671 |
2,368 |
50,008 |
|
B |
178 |
606 |
568 |
16,252 |
|
AB |
99 |
236 |
243 |
5,001 |
|
Ethnic Group — Blood Type |
Hawaiian |
Hawaiian White |
Hawaiian Chinese |
White |
|
O |
|
|
|
|
|
A |
|
|
|
|
|
B |
|
|
|
|
|
AB |
|
|
|
|
a. Fill in the table below with the expected counts.
b. Is there evidence to conclude that blood type and ethnic group are related? Perform a complete test.
11.
On the Titanic, people have theorized that the female passengers were saved while the male passengers perished. Here is the data with the passengers categorized by their gender and whether they survived or not.
|
Gender |
Died |
Survived |
Totals |
|
Female |
126 |
317 |
|
|
Male |
680 |
168 |
|
|
Totals |
|
|
|
a. Fill in the totals in the table above.
b. Fill in the table below with the expected counts. Let your calculator figure out the expected counts (decimals are ok).
|
Gender |
Died |
Survived |
Totals |
|
Female |
|
|
|
|
Male |
|
|
|
|
Totals |
|
|
|
c. Run a complete test to determine if the variables of survival and gender are independent or not. Be sure to provide a clear conclusion.
12.
What are the conditions for conducting a chi-squared test of independence?
13.
The alternate hypothesis of a chi-squared test of independence is:
Observed = Expected
Observed < Expected
Observed > Expected
Observed Expected
Dependent upon the data
14.
Which of the following assumptions are necessary to conduct a chi-squared goodness of fit test?
I. No expected counts <1.
II. Sample size >30.
III. No more than 20% of the counts are <5.
I only
II only
III only
I and III only
II and III only
15.
Given a dataset of n ordered pairs (each an (x,y)), how many degrees of freedom are there?
16.
Given the confidence interval formula:
a. What is b?
b. What is t*?
c. What is SEb?
17.
Here are the golf scores of 12 members of a college women’s golf team in two rounds of tournament play. (A golf score is the number of strokes required to complete the course, so that low scores are better.) To what extent may we predict the second round score from the first round score? The standard error of the slope is 0.23.
|
Player |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
|
Round 1 |
89 |
90 |
87 |
95 |
86 |
81 |
102 |
105 |
83 |
88 |
91 |
79 |
|
Round 2 |
94 |
85 |
89 |
89 |
81 |
76 |
107 |
89 |
87 |
91 |
88 |
80 |
a. Find a 95% confidence interval for the slope.
b. Find a 99% confidence interval for the slope.
18.
What are the typical null and alternate hypotheses for a significance test on slope?
19.
How many degrees of freedom will you work with?
20.
Can a pretest on mathematics skills predict success in a statistics course? The 55 students in an introductory statistics class took a pretest at the beginning of the semester. The least-squares regression line for predicting the score y on the final exam from the pretest score x was . The standard error of b was 0.38. Test the null hypothesis that there is no linear relationship between the pretest score and the score on the final exam against the two-sided alternative.
21.
Here are the golf scores (again) of 12 members of a college women’s golf team in two rounds of tournament play. (A golf score is the number of strokes required to complete the course, so that low scores are better.) To what extent may we predict the second round score from the first round score?
|
Player |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
|
Round 1 |
89 |
90 |
87 |
95 |
86 |
81 |
102 |
105 |
83 |
88 |
91 |
79 |
|
Round 2 |
94 |
85 |
89 |
89 |
81 |
76 |
107 |
89 |
87 |
91 |
88 |
80 |
Run a significance test that there is no relationship between the first round and second round scores.
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